{
 "metadata": {
  "name": "fresnel_integrals"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "%pylab inline",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "\nWelcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\nFor more information, type 'help(pylab)'.\n"
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": "from sympy import Symbol, fresnels, fresnelc, oo, I, re, im, series, Rational, sin, cos, exp, plot\nfrom sympy.plotting import plot, plot_parametric\nfrom matplotlib.pyplot import figsize",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "Plot of the two Fresnel integrals $S(x)$ and $C(x)$"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "x = Symbol(\"x\")",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "plot(fresnels(x), fresnelc(x), (x, 0, 8))",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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XnaDlVxtFzOnpJOZqX1wtzMp2ejzytWgtknDtGtlZ4rFfeX7lfZg8mToQ4esC\n4cL88cfhkbbWgKXy+y86ImXEvGhRaB3rjz6i7XPmkEAdOUKR6rRpFK0KW+rECdpf7JORQe+9cIEm\nwIixgyVLQr3bhgY5h7u1lf49aRI9EaiFWXlvRUaGuNZ16+T7Iwb7PB5ZmEWOfFZWqIUoSvW2tVFE\nPGkSXdeaNbKVcfo0tWP6dLJwxOc4a1Z063I6RpgrKyuRPJAF7/F4UKORTFhRUYHDhw/jNuHYxwm7\nB/6A6CJmK2KrN1imhZ44KjFqb6TMDL1tvb3yoI3W+dQdgd6x9F7XarM4rhjE1Cr6NGeOPGlDiVqY\ng8HQe6cWtcmTKRJWiqPSehAoO72MjNC2qK/txAl6fBZRoDJiV3dQ6r9Pn5Zzn0Wa4pw54cLc3Bw6\n1V0dMQthFu+ZN4+emsRYgiTRvUtICM1AUV6L8jtz6hRlNghLJSODRFE8iS1cGFpGVfjLgCySIqrW\nipgzMsj+EMuitbeT0KemyqlwYmB9woRQz19YLOKYV65QexYtovbl5pI4t7VRep3w0ZXfvSNHqBNo\na5PL5VotMuYYYQ4EAkhRFD7uFKMaCvx+P7xeL8rLy+PaFrtT5Xp7yR4Rj6NmsWJPTJ5MP2D1YJkW\nej6voKeHIgG1V6tsVzQpc8eP04CmelaeaJNaVK1GzGoBBCgVa8MG4/eLAR915KgW5tOn6T6LmXNa\nhZvUxz57ln78YubdlSsU6YkKg+r91fdW/eSiFzED4ZN/fD55gLe9naJudV3t5GSyCERnEgiQnSLS\nOsX5lB2/GEsQA4jKzqqtTe4MlJ+f8rqUTxDi8xGzOtvb6f+nT8vCr0yVE08B2dl07NmzSWDFYsDi\ne3TsGEWr119Pn9epU6ECqY6ss7PlHP3MTNmGOXZMXqNz/34S4wUL5N+QuD5xvGvX6L4oO4RFi6zP\nzHWMMANAMEKFmtLSUhQWFqKzsxNe9WgCgLKyssH/3ray0qYKu60MI0EyQnzwZssomo2wI1kZ4seh\nVwUv2pQ5vShc+WirJCODOhv19VuxMhobw8uLmvWZ9TIyBOIxVTkTTn1stY3R3h468KoWU/X9U1+T\nlYhZKZhqn10Ij/raRQaIyxX6hDBpEn0Wwo7QEiXxb9Ghqwcnhb+rtFgaG2UPPyeH9h83jo4hhF8I\ns7BFpk+Xxc7lImtDRLiiLepZpHpCCsgRs4jCp0+XrRLl5yfeI+6fOK7y+3vyJEXm119Pxzl1yni2\nrB6OEWY9Aw34AAAgAElEQVS32w3/wDe8q6sLqSIpcoCKigpUV1cDAFJTUyFpXKlSmAsKCqJuSzxy\nmK36ywA9Dore3gxmImzxYzNqT6TtRsKcnk5RhpaloifMfj/9wNQrxbjdNNJ97lzo61aEWS2Meu/X\nE2alR6uOyF0u+p4YDQCqz6+2kbTEVXlv1U83ymucO5csBOGXKwVA3dkpP9Np08hKEN8rtTCLoERp\nOQC0uK04vvJcymMrr9dMxKxs46xZoYOZR47Q09uxY7Kwi45SKbLCzujupv1nztSe3q/M6BHnVUbh\nys5DnF+0VdxPj0c+d0oKBS/nz8v3QJJoYonyvFbGigSOEeYtW7YMim17ezuKB5Y4Dgy45h6PB0VF\nRQDI5lgr1vWxmYsXqbc2yvG1SjT+ssDuAcAzZ0Ifx7WI5EEbCfOkSaEDPerjagm+2gdWonX96ogP\n0Pev9YRZ3X61MF++TB2C8nugdazs7FALZOnS0IwFo4E/ILwj07Iy9NL11H658l6pOzv1edWZGeIa\nlEGJ+j0JCeHCpd5PbbVoecx6wqwUcvEZNzfLeePKjlJpSwhhbm8HPv1pum5lOt7KlfTUOn68PDdA\nnPfMGdlqUpYbENcn9vP76fpTUkLPrd6vrY1+XwAJ9MmTIzxizsvLAwB4vV643W7kDkwLEmJcWFiI\nmpoaVFdXIy0tbXC73Rw5QgMlkYrZWyHaiBmwNgC4dGnkSSxm2hLJg164kDxJvdocViJa0Sa9jkAZ\nGQnUER9AP7ZZs0JT2wBtMdV6slBnZgiBUX4PtNqvHgCcPz90HUGtiFl5bydNokhUdGTz5lEEJsRd\neU6xoowye0V5r5UCoP4M1edVC7NWxKxuu/I9S5fKM+6U59KzWsQ97+8PTZXT21/8u74+fOBPva8Q\n5tZW+TupjJjnzJHzosX7xHdOecyFC8nb7umRf3fiHrS3A5/6lH47e3vl76r4vKZMocktmZnUAVjB\nMcIMyB5yaWnp4Gu1isXfSkpKUFJSgscffzxubdD6IcdKLBGz1WJGkax1M22JFDGrPUA1em3WO7dR\nm/RGtNXir3UMsZSXehBz0SIadFJOd8/MpOsRE1f0UuXU3w2rVkZPT/j4xYUL8nsSE0OjYLXoZWSE\nPllkZsqpXTNmUJsDgfD74feHCnN+vtyxKTsl5cC3uu3KqHfhQlpMtq+P7mV6upyBIt6TlkZPAn4/\niVRyMnVAotO7coXaIJ5KlEGIEDllRoYyYp45kz7fCxdosLGhIfTcegWxRM1w8R1XHlNZVlYZCQvv\nWXw3Zs6kc3Z3036HDtF9E9G48glAWChWFioGHCbMTiAewjxUEbP4IhgNFtoRMSvPpYVWm/UG+MT5\njIRZS+QjDZIB+hNOJkygqFOZqzpxIgm4EEQtYdY6h9rKSE2lqNDvl/1L5ffpnXfCbTL1vRR/+/0k\noKKQlHrwEaDrE9Ggy0VipYwIARLPAwdCy47OmCHXr1iwgKJ0IejKaFbP/sjIoI7s2DGqNzFhAnWC\nSvvE5aLCRuKeZmVRepmYjXj0KN1zsUCuxyPbOuJc6lQ50TaXS566nZJCT1EHD9L7enupsxDfYeXv\nYvFi2m/iRLLzlBGzaKPoONraqI3p6RRJi1xql4vuVVsbta2jQ15JXkxqEec9dowE32pGFguzCruF\n2UiQzGAlYk5Kosjk9Gn9fSK1RdQDiFWY1W0+e5Z+DFqzKY06Ai0rQ+scWqJl9FlGGgBUC7PfT4Kh\nrrYnfshiQoQyHU1ka4hx7P5+urfq+6+ekXbDDRRJtrWRAIgIWSsdUD09WkzNVn7OwuaZOFHeTzm7\nTqx9+M47FPWJLBY9KyMYpH2uv55qEgv7QOszSEiQO67MTJpEouUvA6GZHxkZcr2LFSvo3ktS6PGF\nsAKyQC5eTGI6d66cBZWSQhNYzp+n4zY2ygN06gFeZS6zuMZJk2gatvLJSzkTcM8eel8wSBaU+N5k\nZVE0HQxqr9hjBAuzCruFubOTvvgij9UqViJmIHKVuUgRs5ggoFyfzup5tDoTI3vEaJtexGzGyogk\nzEYDgFqpcmobAaD7lJoaGn2Lx2VxfvGeDz+U84aVqO9lSgrlzKpn7mkJn/q9SqEW7W9vD1/8Vv10\ntWQJlcsUA39qWwKgKHf9ernjz8oioRXn0RscFVaPmLghrunkSaprrWTDBmr/1Kn0WZw7RxFrRwfd\nZ+W9U9oxK1aQ4IoOR9kOl4tys0Wt7uZmOUDQipgPH6ZOobaW6oQAdB7lfjfcQO1fsoQ++zVr6O/u\nbrk2idtNNU7EepNWYGFWYbcwxxItA/RlDAa1V43QQl1nQI2ZVDkz7TUTMSstFb370NND0bSYcKFm\n7lzyXNUrYJgVZr1rycsLv6dGwmz0vVAPAC5bRp+BVg7zjTeGv19LXFtbQwfJ9K5n0SISADHoKyLm\nP/9Z3rexMXRFb4C+VytXyhMzliwhu0P4y+LeqFMYxQxCca6WFrmNkYQ5Kys06t2/X36aEEyfLtdz\nXruWvhciG0Rd5Gr+fHkad3o6ZVTNmaO97223yffz0iW6zr4+Cpq0fHSXi4758cf0pLN7t1xICpAn\nw1x/PUX5ouLeXXeFnjcpiaJmqyshsTAr+Phj6qH1RCIaYvGXgfCZWpEwEszLl+kHZ1Ss34y/HOk8\nbjf5hsr841OnKMJRE2kyS0JC6OCYQHlP9OwiIzGdNSu8rrOIpjo7yadUruRtJPJaA4AtLfSacqCv\nqSlcIAFq44kTsh0iojZ15DdhQngbxo2j7634LLKy6DyXL5NIAdoTplwuOp/oiJYsoWOIiFmSKAtB\n/YSwdKnsaYsKcuLYR4+GihdAg2RiNmpmJn0nhGd86VL4Wol5eXIGw8WLcmQrSaFLZIlji+/YxImU\nppaQQPdSPQ8hLY0i4HHjyOKYOpXu75UroVH40qVy/YtJk+QC/rfeGvrZLVtGxxPXISrgqeu9bNwY\n3bp/LMwK2tspArEzVS7WiBmIbgBQi/Z2ejQzKtZ/7py2gKpJTzcu5K/uTPbvp+hCjZn7o1VoZ8YM\n+lF1d4dPlRYYCbPW2oEiYhbRslKUtGwEgXoAULS3pSX0PXozSqdOJfuoo4P+nj+f2tfRIe//0Udk\nNWjl1y9dKkeZixfTU8jixXL7Ozq0PU6lyC5eTNGzOF9Dg/bvYO1aOcpOT6cOV0zBbmsLP092NnUo\nvb307+5u+o0Fg8Abb4SLbVaWXCBp3DjZF/f5wu/d0qXkcX/8MXXeQiDPnJHbJFi9mu5/MEjtuXaN\nrnFgusQg8+fTto4OeRXz/fvDr2vJErKlGhvpe33pEh1f/dvJyaHvmboOSyRYmBU4LSNDYGUA0GhN\nvrY2eQRcj337QiNFPbQyG5So26y3lJUZ60QtfAD9aNato/dribtIxdIbDRfpccoZimlp1Gnt2xfe\n1kgRs1qYW1vDa3ob1fheskQW18REitr37JHFSEz80BJLpTCLwbM1a+Tte/eGCyBA90/4xdnZJC7i\n+9/WRiKsRtw3gJ68Jk8mMbtyhSJI9XmmTKFORxRKGj+exPPkSRJ2dYSZm0tZE729JGZi9e+LF8Pb\nM2kSvebzkcimpNB5zp8PF8i8PPruHzhAA5xiHcWcnND9XC5g0ybqNMaNo46kri7cI05MpGv9+c/p\nGHv30m9B7ZmvX08BkdbqMkawMCsw+vFFy1BHzCJpXitlzkxbrC4YayYzQ29hV8CcMKutAkFKComd\n1nUJi0TP25s0iX5syqL+opjRnj3hEVJnp/59UbcvOZlSuc6fDxXi8eP1a7AsWxa6YOmiRfKjNEDb\ntMQVoOtQvnfhQjnn9vx5eckkNZmZcgH7q1fpXok622fPap8vJ4c80/5+edbc0aMkjHffLc96U5Ke\nToLo88kLs+7bR+1WWyVutyy2R4/S8draqAPRmlN2xx1kSQUC5JlXV1MEqx5sT0qie/rsszTA2NBA\n5xDZGUo2bABeeIF86dmzgV27gIF5biHcdx+17dFH6XO6+Wa5vKzyev7pn4BHHgl/vxEWLenRTVub\n/pc/WuyKmH/1K3P7JifTj+Xs2fAvyZEjxjVAjARUr11tbRRhqMnIkH/0nZ10bHWqGUCCNlCCW5fs\nbIpM1AjrYfz48AjJzNNPaio9yiv3E4Ngd9whv3buHAmD8GzVLFxI9/vyZVmYAgESOWGvXL4MvPYa\n8Nvfah9jzZrQ8pULFoSKqSRpDxwC5NP+8pfy35cuyaliBw9qCyBAUeT58xTBNjXRd6e+Xq5RrJVJ\nkJZG19XQQMdOT5ftBL2UsPx8iijPniVhP3CAIumByb5hbNpEArtuHVkS3/2uXINZa9/HHqPf7d/9\nHfCznwGK+WkhPPgg8NxzwNatwJtvak/2Achbd7vpvvb10f3UspBuvZWyM8aPN/4Of/rT+tv04IhZ\ngd1WRqSMA7NYGfwD9CPZSE8E585R1KQeibd6HrFNtFmIvZY4mCkYJawC9VOAEGafL3xA08xnqbQA\nlMc8fjxUZA4doohWq/0APdaKFDlBZmbovT50iKIuPSspOzt0KvdHH8nr+QHkeeoFDUuW0Cy8zk6K\nZBMS5Nzi+noSOC2Sk0nwfD4S5tWr6d8HD1IEqDUmAACf/CS1dd8+ijjr6kh4lfaJksJCin5raoAv\nfYnu+e7d4f6uoKSE9rnvPuB//2+6v5/9rPa+a9YAP/gB8K//CmzZAmzfDjz0kPa+69cDL71E9+sf\n/oEEXYvERBqLSUkhW085MUeN1YqRZuGIWYHdwnz0qHHGgVnmzCG/7dKl8BxYLYRg3nJL6OuRrAwr\n0bI4j3IlCyUZGXKOqd5xe3rI6zP64gMUpSUmUseh9L+XLAF+9COKRtWRT1dXuH+oZtkyivaUZGXJ\nA1WCxsbwwSQ1ovMQ57x4MXSJqOZm4+vMySFRFFH35csknMIDP3ZM/3oSE2n0f+dOelzPzqb7eu0a\nCfPdd+ufd9UqugdtbbTfW2+Rv3rDDfrvuece4FvfIn/4sceAL3+Zngz0hHbWLODv/56i88JC2rev\nT/9+ZGQAv/ud3Ik9/7x+W4BQ79nqRA6nwsI8wNWr0RWzN8IOfxmgCEgUqBHTQo3QyjgQ01SNxCEa\nYdaLmGfOpAiuq0v/uG1tJCSRBiQB+tG3toYK8+LF9EitNbPq3XeBf/kX42OuWEGeo5KJE0lUlRke\nkqQ9EKZErHEnmDIldF3EnTvDU8PU5731VvK3N2ygiHnePHrsd7lIrI0GZT/1KRp86+igKPLECeCP\nf6To36gC7l13kbjOnEniefw41Vv50Y/033PTTcC//zv5r7NnU5Q6bpy2vyy4917533oRvBIz34nR\nDAvzAGLevp2PJnb4ywIxAGhGmDMzgT/9KfQ1veprSqwKs3JVC/VTQUKCnBd8+LBcmUuJlZXIp06l\n6E85WDN1KkXT2dmhohAMhlYl02P5cnr/1avy5y5WTO7pkVO19uwxjjoBum8vviifXwyQnT1Lgnrs\nGPDww8bHKCqiiNXtpkyG3Fzy6RMT9W0CwSc/CXzlK9QBf+c7dL4f/5hqVRiVeM3JAZ5+mvz2yZOB\nsjJ6MotkZynFfvZs430Z67AwD2CUpxrLMe3K8rCSMqcVyZrNyFBGNpEQa9x1dGiv46fMk9XyR60I\n88qV2ilHs2eHL3R55gxFuOpULDWirkh9PfmrAHU0aWl0L1auJNH2+fQHqgTr1wOf+xztf+wY2S53\n3UVe7C23kGBGslY2bQK+9z2KkNeupQHIrVtJmL/3PeP3LlgA/PM/U6S9Zg1dT16eufENpehPmGDc\neTNDAwvzAPHKYVavNxctGRmho/ZGKOsgiAErMx2P1YgZII+ypUVbmG+8kR6pX30V2LYtfLvebEC9\n8+zbF/56amqoZQCQkPb26g/WKbnlFuCDD2RhPnKEHtWbm+WBsbvuogjWiNRUilrffpuevj7/eep0\nXnuN7Jy1ayM/nq9aRVHyvn3AT35CHctXv0p+rJny46KuA0DXbtfTGjP0cFbGAE6rw6zGSi5zSgqJ\nonJK9JkzxoVUrKbKKdt16JD2tgUL6FE8OVn7cfr9982vrZiTA/zhD6HL2gPkY4sptIL6evOCv2GD\nfF+vXKF/b9xImQYAibbZFMo776RR/7feIgvh3nup06iuBu6/39wxnnwSqKyUo/0774xsozCjDxbm\nAeJR7lOsTGwHVqwMl4tmLClX5KitNa6RoVzo0grLl4ennAnEIpnq+gkA+dJNTZF9YEFKCo3oq2cA\nJiaSJaEU7F27InuygvXrqWPp66PshDlzKO/U5yNbQgzGmWHzZmrn2rV03KlTgf/4D+CHPzTfHpfL\n3pIAzMiEhXkAu2f9ifKZkR6BzSIWktRbzkmN0t8FIvu50UTLAAmzMt9WyYIFNPCl5a22tVEmgJX7\nM3Mm1S0QnDhB7Q4EZJvn2jUSU3WqoB7z55NP/frrwI4dFC1nZFDbv/QlEkmzx5o4kYT4scdkG2XW\nLHsX9mXGBo4S5urqani9XlRUVBjuV15ebut5+/powMZOT87OjAyA/MmlS6mdZlAK89WrNEBnZw6z\nYOVKEjStVbFdLjnLQU1jo/UZUatW0UQGwd/+Rjm1GzcCf/0rvbZ/P12n0dOBmgcfpLS5tjbZcvjW\nt2jwTAy+McxQ4hhhrhsw9QoH5jb6fD7N/WpqarBjxw5bz93RQZGdcoWHWLHTXxbMnh1qTxihFGZJ\nosjQKBUwWmF2uymS1aplAZAoay0Q+/775oolKdm4kWwKMQOwvp4mQnzmMzTFFqDBNq0p4kbcfjtl\nPYi0MYCeUB57zFx6IsPYjWOEubKyEskDlUc8Hg9qamo093OZGWq3iFOryqkx8nPVKIXZTFpad7f5\ngTg1eXnkyarp6SH/98MPw7ft3Rt50oaaxYtJOOvq5HXsNm6k//r6KCPiwAGKoq3gcpEHbHdHyjDR\n4hhhDgQCSFFktXdqGJc+n28worYTp+cwC9QVyIxYtIiu6cIFEuZIU1XffTf66awbNoRWaRPU19OA\n4s6doXUu+vrImjE7ICYQi3tWVdGU3Rkz6B6PH08VvL73PeokOMplRjqOEWYACBot7wzAb3Z9JYvE\nI2Lu74+PMOulpqlJTCRRPnQocsR89SoJa7TCvGwZDZ6pqa+n6HXt2tAp4gcOUJ6xelkhM3zuc+Sz\n//d/U40Gwd13UzpdpGnYDDMScMwEE7fbPSi8XV1dSFX9as1Ey2VlZYP/LigoQIFRkQAFbW3hi1XG\nSk0NVb2yk6VLyWMWFcQikZNDlcJaWvSrcwHkDy9cGP2Mr3XrKApWTmMG6B4UF1MO9RtvyML/zjuR\nZ8Hp4XYDFRXU6ainApsp8MQwIwHHCPOWLVtQW1uLwsJCtLe3o3igVFUgEIDb7YYkSZAkCZ2dnfD7\n/fD5fMhTzZNVCrMV7I6Yu7up3kCkKcFWmT6dJmscP649007NqlWyMBtFzK2tofWHrSLSAvfupUI8\nAFkXH3xAtXTT0sh+EFRXUxGcaJkyhUWYGd04xsoQIuv1euF2u5E7MAe1aGDpgJKSEpSUlMDlcqG7\nu9u2QcD+fvMrQ5tFeNZxGKe05DPn5ND03uuvN+4kamvDV3ywypo1FCELxIobHg+tBNHcTFOVGxsp\n73njxtjOxzCjGVcwkrE7QnC5XBE9ai1OnCAPVNQOtoPKSlqporravmMKvv51ytF9/PHI+54/TxbF\nypUUverxqU/Rqg9WsxmU7N5N9SEOHSKb5Uc/ohoR4iGmvJwi8/5+mi79j/8Y/bkYZrTjmIh5uHB6\njQw1a9aYr5mRlha+RJEWygLv0bJuHU0/r60l8X399VB75J/+ie7J4sWhg3YMw4TjGI95uOjoiF2U\n1LS1Ga8AEQtLltBECLNcuaK9Vprg7Fma0mzGszbC5aJaEc8+S/czNTX0HkyaBHzzm7Gdg2HGCmM+\nYm5qsr/QdzyicMGKFRSRq0tdGmHkddfWUu6vmSyPSHz2s3LmSFlZfDx2hhkLjPmI+ciR2LxVLeIp\nzBMm0NTphobIEzTEytRGg4VNTeaL9EQiMZHziBnGDsZ8xHzkiL1Tpy9dosI98+bZd0w1elOg1Rw/\nTlbNoUPa9SoAKv5jtnYxwzBDw5gXZrtT5SSJBsHssAb0yM01J8x1dSS6YpFPNX19VEzI7sk1DMPE\nxpgW5q4uKlcZzdRgPeJpYwjWrKGVnCPh85Ewr1hBAqymro5WOklLs7+NDMNEz5gWZlEBzs5BqqEQ\n5rw8ypHWsycEHR0kvMXFwCuvhG/fsYMq1jEM4yzGtDDHI994KIR5yhTKBzayM/r7SYzz86n62+TJ\nVLNCyRtv0EKjDMM4izEvzHbXTB4KYQZIUA8c0N/e2koLoM6eTZkcCxfSatWC9nYqlylqWzAM4xzG\ntDDbPfAHDJ0wL18O/PnP+tv37Akd1HvwQeCXv5SXeXrpJfKex42LbzsZhrHOmBZmuyPmnh7g9Gma\nBh1vNmyg4vZ9fdrba2pCV3e+7TYqmfnii1TP+I9/BL72tfi3k2EY64xpYbY7Ym5vJ8vguiGYtjNz\nJvnHysVJBcEgCfNAYT4ANMD5/e9TgaWvfAX4whcorY9hGOcxZmf+Xb1KFeXsjG6HysYQ3HAD2Rk3\n3RT6+qFDVFND/TSwciXwP/9Dk2DsnobOMIx9jNmI+ehRmp1nZ3Q71MJ8331kZ6irnVZXU5F8rTRA\nMSDIMIxzGbPCHI+Bv3iW+9RizRpagXrfPvm1YBB46y2q9MYwzMhkzArzSE6VE7hcwGOPAdu2ya/t\n3EmZF/EqO8owTPwZ08I8UlPllDz4INkyBw7Q9PLt26kQfTxrdTAME1/G7OCfJNlX7hIAentpCnSs\nBeetkpxMQvzYY5QRMm0a8NBDQ9sGhmHsZcwKs90R87FjwJw5NMtuqNm8mSL106dpkdPExKFvA8Mw\n9uEoYa6urobb7YYkSSgtLQ3bXlVVheTkZLz88sv4+c9/HvV5gkG5gJFdDIeNoYRrKjPM6MExTmRd\nXR0AoLCwEADgU1Xo8Xq98Hq9KCwshCRJ2L9/f9TnOnOGivokJUXfXjXDLcwMw4weHCPMlZWVSE5O\nBgB4PB7U1NSEbC8sLMTPfvYzAIDf70dubm7U5xotA38Mw4xOHCPMgUAAKSkpg393dnaG7dPd3Y3y\n8nI8+eSTMZ3LbhsDYGFmGMY+HOUxB9VT2FRMnz4dW7duxaZNm5Cfn490VbGHsrKywX8XFBSgoKBA\n8zgcMTMM42QcI8xutxt+vx8A0NXVhVTVek91dXVwuVzIy8tDfn4+qqqqsHXr1pB9lMJshCRRtTW7\nuHaNcontjsIZhhmbOMbK2LJlCyRJAgC0t7ejuLgYAFkcAA3+CeEOBALIiCHktXvWX0cHcP31wKRJ\n9h2TYZixi2OEOS8vDwAJsNvtHhzcKxqoXfnwww9DkiRUVFQgOTkZ9913X9TnstvKYBuDYRg7cQUj\nGbsjBJfLFdGjBqjkZVoa/d+uacs//zkVEqqosOd4DMOMbRwTMQ8VkkQF4u2sJcERM8MwdjImhdnu\nQbqhLvfJMMzoZswJczxE9MwZIDvb3mMyDDN2YWGOkb4+wOcDsrLsOybDMGObMSfMdlsZR45QVTlO\nlWMYxi7GnDDbHTE3NdHCpwzDMHYxpoT52jXg+HF7i9k3NwNLl9p3PIZhmDElzCdOUA6znbZDUxML\nM8Mw9jKmhDkeC7CyMDMMYzdjSpglyV5/ORgkK4M9ZoZh7GRMCfOZM/aK6MmTZIsoykgzDMPEzJgS\n5oMHgfnz7TseD/wxDBMPxpQw253DzP4ywzDxYMwJs905zCzMDMPYzZgR5kAAuHqV0uXsgieXMAwT\nD8aMMAsbw+Wy75jsMTMMEw/GnDDbRSAAXLwIzJtn3zEZhmEAFuaoETaGnRE4wzAMMMaEmQf+GIYZ\nCVw33A1QUl1dDbfbDUmSUFpaGra9YmBRvSNHjuDpp5+2dGxJAu65x5ZmAqCVsdets+94DMMwAsdE\nzHV1dQCAwsJCAIDP5wvZ7vV6UVRUhNLSUkiSBK/Xa+n4dtfJ2LWL1g5kGIaxG8cIc2VlJZKTkwEA\nHo8HNTU1IdslSRp8zePxQJIk08fu66PKcgsX2tfeAweAnBz7jscwDCNwjJURCASQoig60dnZGbJd\naW3U1dXhgQceMH3sjg5g1ixgwoTY2wlQzY0rVzgjg2GY+OAYYQaAYDAYcZ+6ujqsXr0aubm5YdvK\nysoG/11QUICCggIA9mdk1NcDq1ZxRgbDMPHBMcLsdrvh9/sBAF1dXUhNTdXcz+v14qmnntLcphRm\nJXYL88GDbGMwDBM/HOMxb9myZdA3bm9vR3FxMQCyOATbtm3D1q1bAcDS4J/dA38szAzDxBPHCHNe\nXh4AEly32z1oVRQVFQEAampq8M1vfhOZmZlISUmBy4KPYHcOMw/8MQwTT1xBM8buCMDlcul61GvW\nAD/9qT15x729wPTpwLlzwJQpsR+PYRhGjWMi5nhip8fc2krF9lmUGYaJF6NemLu6KI9ZZyzRMuwv\nMwwTb0a9MNtd7pOFmWGYeDMmhJkH/hiGGUmMCWG2y18OBoFTpwCNuS0MwzC2wcJsgRMnSJgXLLDn\neAzDMFqwMFtgzx5KueOp2AzDxJNRL8xHjtjnMe/ezTWYGYaJP6NamHt7gZMn7bMe9uwBbrjBnmMx\nDMPoMaqFuaMDmD0bGD8+9mNduwbs20ezCBmGYeLJqBZmO/3lxkZgzhxgoJY/wzBM3GBhNokY+GMY\nhok3o16Y7Rr4Y3+ZYZihYlQLs511mDliZhhmqBjVwjxunD0R8+XLVFVu1arYj8UwDBOJUS3Mr70G\npKfHfpy6OmD5cvsWc2UYhjFi1ApzVxfQ3w8oFt6OGvaXGYYZShwlzNXV1fB6vaioqNDd54knnjB1\nLDHwZ8f06ePHgZtvjv04DMMwZnCMMNfV1QEACgsLAQA+ny9sn23btqG6utrU8exKlQsGgd/+Frjp\nphfamREAAAfESURBVNiPxTAMYwbHCHNlZSWSB2ZveDwe1NTUhO3z8MMPw2NSbe3KyGhtpZmDixbF\nfiyGYRgzOEaYA4EAUhSGcGdnZ0zHsytifvttoKAg9uMwDMOYxTHCDEB3letosEuY33mHhZlhmKHF\nMcLsdrvh9/sBAF1dXUiNcfVUO4Q5GKSIecOG2I7DMAxjheuGuwGCLVu2oLa2FoWFhWhvb0dxcTEA\nsjjcbrepY5SVlQGgNLmOjgIsWFAQU5taW4G1a+3JhWYYhjGLYyLmvLw8AIDX64Xb7UbuwMJ6RUVF\ng/tUVVWhtrYW27dv1zxGWVkZysrK8PnPl2Hu3IKYy32+/jowYwavWMIwzNDiCtpp7A4jLpdr0KPe\nsQN46ingzTdjO+YddwAPPwzcd58NDWQYhjGJYyJmO7Gjqtzly8B77wEDadUMwzBDxqgV5lgH/t55\nB8jPB6ZPt6dNDMMwZmFh1uG118jKYBiGGWpYmDUIBoH2duDTn7avTQzDMGZhYdagthZoaQFWrLCv\nTQzDMGYZdcLs98de7vOll4AHHuA0OYZhhgfHTDCxCxEtRyuq/f1AZSXlMDMMwwwHoy5ijtXG2LUL\ncLtpxRKGYZjhYFQKcyw5zL/9LdkYDMMww8WotDLy86N7b28v8PLLwM6d9raJYRjGCqMyYo7WyvjT\nn2ilksxMe9vEMAxjBRZmBT/4AfDQQ/a2h2EYxiqjSph7e4GTJ4EFC6y/9/33gVOngHvvtb9dDMMw\nVhhVwnz8ODB7NqIq9/mDHwBf/zqQmGh/uxiGYawwqgb/orUxJImKFv3qV7Y3iWEYxjKjKmKOVph/\n+EPgy18Gpk61v00MwzBWGfMR8+HDwAcfAK+8Ep82MQzDWGXURcxWJpcEg8Cjj9KEktmz49cuhmEY\nK4wqYT5yxFrE/OtfA4EA8NWvxq9NDMMwVhlVa/4lJQUhSUBqauT9T56kySR/+EP0MwUZhmHigaM8\n5urqarjdbkiShNLSUsvbAXPlPi9cAO66C3jsMRZlhmGcR1RWxttvv21zM4C6ujoAQOHA6qc+n8/S\ndsBcuc+eHuCee4AbbwS+9rVYW21MPO5TrHCbzOPEdnGbzDHS2+QYYa6srERycjIAwOPxoKamxtJ2\nel3/+MEg8Ne/UqTs8QDPPhv/Qvgj/csxVDixTYAz28VtMsdIb5NjrIxAIIAUhQ/R2dlpaTugLczB\nIOD1At/+Nq1u8u//DmzezDP8GIZxLo4RZgCINA4ZafuiRUBnJwmw3w8cOwY89xxw5gwJ8gMPsCAz\nDON8osrKcPFieAzDMJYxK7dRRczxyLDz+Xyora1FaWkpysvLUVxcjNzcXAQCAbjdbt3tDMMwow1b\nJpg88cQTMR8jLy8PAOD1euF2uwdFt6ioyHC7k7HjvjDDS3l5+XA3gRmLBGPkF7/4RTAjIyPWw8RE\nVVVVsKamJrht27ZhbYcSJ9wXNdu2bQtu27Yt+MQTTwx3UwZ5+eWXgzU1NcFHHnlkuJsSxo4dO4LF\nxcXD3YxBvvGNbwSDwaCjvuf79u0LVlVVOaZN+/btC7pcrmBGRkYwIyPDMd8rqxoVc8T88MMPwxPL\nstQxYia/eTgY7vuixuv1oqioCKWlpZAkCV6vd7ibBK/XC6/Xi8LCQkiShP379w93k0Jw2lhKRUUF\nsrKykBHLasM28/TTT6OkpASBQMARv72uri709/ejra0NL7/8Mr75zW8Od5Pg8/ng8XhQWFgIj8dj\n6j6N+FoZZvKbGUCSpMF74/F4IEnSMLeIOtOf/exnAAC/3+8oe8rn8w129k6hoqIChw8fxm233Tbc\nTQEAVFVVYe3atQCArVu3DtqNw4nyM6utrcWiRYuGrzEKhK0pSZKp+zTihdlMfjMDlJaWDk5jr6ur\nG/xBDTfd3d0oLy/Hk08+OdxNCcHv9w93E8Lw+/3wer2O8b1ra2vR2dkJn8/nmDYJvF4vNm/ePNzN\nAEDjY+np6UhJSQnRKiMiZmVUVFSEvZaSkoKSkhLrLYwTwdFRh2lIqKurw+rVqx0TnU6fPh1bt27F\npk2bkJ+fj/T09OFukiOjZQCDHeuOHTsGLaDhJi0tDXl5eaipqUF1dbVjdGHHjh2OuD8ABY+ZmZmo\nqKhAaWmpqe95RGHWKxbkFNxu92B009XVhVQzpeXGMF6vF0899dRwNwMAdRIulwt5eXnIz89HVVUV\ntm7dOtzNgiRJkCQJnZ2d8Pv98Pl8w/6YXlFRMRgQpaamQpKkYRee1NTUQYFxu93Yu3evY4RZjD05\ngYqKCjzyyCNISkqC2+029T2P2cqoqqpCbW0ttm/fHuuhomLLli2Dfml7ezuKi4uHpR1qhvu+aLFt\n27bBL4RTBv9EpxoIBBwzqFVSUoKSkhK4XC50d3c7YhDQ4/EMpo52dnY6woq6//77B397gUAA69at\nG+YWEU4YP1GTlJQEgDxwt9sdcf9RUY+5oqJicEDL6RH+cFFTU4PNmzcjJSUFfr8fVVVVwz6I1N3d\njcrKSgD0Y3JKJO9UqqurAVAA8vjjjw9zawgRydfW1jrm82tvb8czzzwzOLDsBMrLy+HxeOD3+01p\n1KgQZoZhmNHEiM/KYBiGGW2wMDMMwzgMFmaGYRiHwcLMMAzjMFiYGYZhHAYLM8MwjMNgYWYYhnEY\n/x9TP3s0txWEHwAAAABJRU5ErkJggg==\n",
       "text": "<matplotlib.figure.Figure at 0xa3be80c>"
      },
      {
       "output_type": "pyout",
       "prompt_number": 4,
       "text": "<sympy.plotting.plot.Plot at 0xa3be1ac>"
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "The Cornu spiral defined as the parametric curve $u(t),v(t) := C(t), S(t)$"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "figsize(8,8)\nplot_parametric(fresnelc(x), fresnels(x))",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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+cadGDQbk/Pm8Xa8ecMMNnBQ1cCAnJ3XrxsC9/35WXo4uW8e4rmOmsU+R/9GX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\nhBBiJyi6hBBCiJ2g6BJCCCF24v8BBiDuvbcyGUYAAAAASUVORK5CYII=\n",
       "text": "<matplotlib.figure.Figure at 0xb22c34c>"
      },
      {
       "output_type": "pyout",
       "prompt_number": 5,
       "text": "<sympy.plotting.plot.Plot at 0xb22c76c>"
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "Compute and plot the leading order behaviour around $x=0$"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "ltc = series(fresnelc(x), x, n=2).removeO()\nlts = series(fresnels(x), x, n=4).removeO()",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "lts, ltc",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 7,
       "text": "(pi*x**3/6, x)"
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "figsize(4,4)\nplot(fresnels(x), lts, (x, 0, 1))\nplot(fresnelc(x), ltc, (x, 0, 1))",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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       "text": "<matplotlib.figure.Figure at 0xd493acc>"
      },
      {
       "output_type": "display_data",
       "png": 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       "text": "<matplotlib.figure.Figure at 0xecaf34c>"
      },
      {
       "output_type": "pyout",
       "prompt_number": 8,
       "text": "<sympy.plotting.plot.Plot at 0x101b4bec>"
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "Compute and plot the asymptotic series expansion at $x=\\infty$"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "# Series expansion at infinity is not implemented yet\n#ats = series(fresnels(x), x, oo)\n#atc = series(fresnelc(x), x, oo)",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "# However we can use the well known values\nats = Rational(1,2) - cos(pi*x**2/2)/(pi*x)\natc = Rational(1,2) + sin(pi*x**2/2)/(pi*x)",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "figsize(4,4)\nplot(fresnels(x), ats, (x, 6, 8))\nplot(fresnelc(x), atc, (x, 6, 8))",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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nUDVnFFVdgZhwyt4Ii4tiqjtFlxtR/4CsoItef5mKwclJ69e6uFhNBZsyQRft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\n/r0TkFbd33iD2WcqO4kkws0EvVrk4WF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       "text": "<matplotlib.figure.Figure at 0xd61d64c>"
      },
      {
       "output_type": "display_data",
       "png": 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smiIq5MGTGiyqJn1tzf4DD0Sz+XhWG9ZkHVrUwzPRsCRNVVXxPYcs6b5er1j/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\ndBeXfYAr6C4u+4D/D7yUXoFdkz+AAAAAAElFTkSuQmCC\n",
       "text": "<matplotlib.figure.Figure at 0xff9556c>"
      },
      {
       "output_type": "pyout",
       "prompt_number": 11,
       "text": "<sympy.plotting.plot.Plot at 0xda47a8c>"
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": "Another nice example of a parametric plot"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "alpha = Symbol(\"alpha\")\nr = 3.0\ncirc = r*exp(1.0j*alpha)",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "figsize(8,8)\nplot_parametric(re(fresnelc(circ)), im(fresnelc(circ)), (alpha, 0, 2*pi))",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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ZvVu/ORQZ4/x3spMTHS3StCkLPugpENeupTnt8OH0f28yiSxZwuCo1193n7q+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\nhUWaYRiGYQyU/wdTZyvgq7IG/AAAAABJRU5ErkJggg==\n",
       "text": "<matplotlib.figure.Figure at 0xedd43ec>"
      },
      {
       "output_type": "pyout",
       "prompt_number": 13,
       "text": "<sympy.plotting.plot.Plot at 0xb15a4ec>"
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    }
   ],
   "metadata": {}
  }
 ]
}